Open AccessSemantic Decision Procedures for Some Relevant Logics
Author(s) -
Ross T. Brady
Publication year - 2003
Publication title -
australasian journal of logic
Language(s) - English
Resource type - Journals
ISSN - 1448-5052
DOI - 10.26686/ajl.v1i0.1760
Subject(s) - decidability , semantics (computer science) , set (abstract data type) , description logic , mathematics , t norm fuzzy logics , range (aeronautics) , reductio ad absurdum , computer science , discrete mathematics , artificial intelligence , theoretical computer science , programming language , interpretation (philosophy) , fuzzy set , materials science , membership function , composite material , fuzzy logic
This paper proves decidability of a range of weak relevant logics using decision procedures based on the Routley-Meyer semantics. Logics are categorized as F-logics, for those proved decidable using a filtration method, and U-logics, for those proved decidable using a direct (unfiltered) method. Both of these methods are set out as reductio methods, in the style of Hughes and Cresswell. We also examine some extensions of the U-logics where the method fails and infinite sequences of worlds can be generated.